What is the difference between inequality and inequalities?

The difference between "inequality" and "inequalities" is primarily one of grammatical number: "inequality" is singular, referring to a single instance of a non-equal comparison, while "inequalities" is plural, referring to multiple instances.

Here's a more detailed breakdown:

• Inequality (singular): Refers to a single mathematical statement that compares two expressions, showing that they are not equal. This comparison uses symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

  • Example: x + 2 < 5 is a single inequality.

• Inequalities (plural): Refers to a collection or set of two or more inequalities. These inequalities can be related (e.g., part of a system of inequalities) or unrelated.

  • Example: x + 2 < 5 and y - 3 ≥ 1 are two separate inequalities. A system of inequalities would be x + y ≤ 5 and x - y > 1.

In essence, "inequality" is to "inequalities" as "equation" is to "equations." The plural form simply indicates that there are multiple instances being considered.